Abstract
The propagation of longitudinal and shear elastic waves through a multi-phase material was studied and the effective elastic properties of the medium were evaluated. The distribution of the reinforcing inclusions was considered random throughout the matrix. The effective dynamic properties of the composites, including their effective bulk and shear moduli and effective densities, were examined along with the effective phase velocity and attenuation of the incident P and S waves. The Sabina–Willis model was employed to study the wave propagation behavior, and the model performance was analyzed through comparison with experimental data from the literature. The results indicated that wave propagation significantly depended on the physical and mechanical properties of inclusions relative to those of the matrix and the normalized wave number of the propagated elastic wave. Moreover, despite the fact that the elastic properties of the incidence in the P and S waves exhibited a similar trend, their values differed significantly. The results can serve as a design criterion for composite materials under dynamic loading.
Highlights
Having a wide range of industrial applications, composite materials have become quite prevalent owing to their substantial lightweight and the fact that their mechanical properties can be tailored to intended loading situations
If the elastic property tensor and the density of the matrix are represented by L2 and 2, respectively, and the properties of the spherical inhomogeneities inside this medium is represented by L1 and 1, it is assumed that any inclusion inside the medium is placed in a homogeneous medium having the final properties of the entire composite material, i.e., Leff and eff
It is observed that the model provided a better prediction of wave propagation behavior at lower normalized wave numbers
Summary
Having a wide range of industrial applications, composite materials have become quite prevalent owing to their substantial lightweight and the fact that their mechanical properties can be tailored to intended loading situations. Berryman (1980) analyzed the wave propagation through a multi-phase medium to determine its effective static properties His approach was to set the scattering wave field equal to zero to determine the final elastic constants. Sabina and Willis (1988) reported the first classic self-consistent analysis using an effective medium approach, which yielded acceptable results at high filler concentrations In their approach, the mean wave properties were gained through an iterative method. Compared with the Waterman and Truell model, the analytical results reported by Kim et al were more consistent with Kinra’s experimental results These methods presented zero-frequency elastic properties similar to those obtained from Hill and Budiansky’s static analysis. The Sabina–Willis model results were compared against published experimental data
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